Miyamoto

Basically, Miyamoto graduated from college with no job lined up. His father was friends with the president of Nintendo, so he arranged an interview with Nintendo, which was in the transition from making hanafuda cards to making games, to eventually making video games. Miyamoto showed up with a suit and some experimental toys he created. Basically, he was mainly given the job from his family connections.

A few years later, Nintendo of America decided it was time to push all in, on a modest hit in Japan called Radar Scope. Most arcade games at the time were simple variations on Space Invaders; Radar Scope was no different. The game took far too long to arrive from Japan, and Nintendo of America was stuck with an abundance of arcade cabinets and boards they could no longer sell. This was almost all of their assets. NoA's president, the son in law of NoJ's president, basically had to beg the NoJ president to do something and make a new game. Yamauchi, NoJ's president was kind of a dick. He basically had told NoA that it was a bad idea to order that many and that the game wouldn't be the hit they'd expected. He threw Miyamoto, who was an apprentice in the planning department with making a new game using the boards from Radar scope. Miyamoto was chosen because "everybody else was too busy". Miyamoto made Donkey Kong.

Funny story about Donkey Kong's success: NoA thought it was a joke initially. They thought NoJ was actually trying to punish them for being stupid, and the consensus was that the game was terrible. One guy working there at the time even quit because he thought the game was so bad it would push the company under. Then the game started devouring quarters from just about every test location they put it at.

From then on, Miyamoto had proved his chops as a game director and developer, and you've probably heard the stories on how Zelda and Pikmin, for example were made.